Lattice design for subaperture stitching test of a concave paraboloid surface

Lattice design is subtle and complicated for the subaperture stitching test of aspheric surfaces. Methods are described in this paper for the collection and arrangement of subapertures, and calculation of the best-fit sphere for each subaperture. The best-fit sphere is determined by minimizing the mean-square aspheric deviations in the form of a surface integral. Finally, a numerical example is given to illustrate the procedure, and also to verify the validity of our proposed methods.     

Testing of large optical surfaces with subaperture stitching

Based on our previously proposed subaperture stitching and localization (SASL) algorithm, we present strategies and a prototype for testing of large optical surfaces with subaperture stitching. First, several strategies are introduced to deal with new problems when applying the SASL algorithm to large surfaces. The uncertainty of the lateral scale of the interferometer is compensated in the same manner as that of the radii of best-fit spheres in the algorithm. Then the coarse-fine stitching strategy is proposed to stitch tens of subapertures efficiently. Second, a prototype for testing of large surfaces with subaperture stitching is developed with a welded structural base. The model of kinematics is built to determine the initial configuration of each subaperture, according to the records of nulling motion. The uncertainty of linear motion is required to be no more than 1 mm, taking advantage of the large range of convergence of the SASL algorithm. Finally we present an experiment to verify the validity of the method and the prototype. A spherical surface is tested and successfully stitched with 37 subapertures.     

Precision analyses of a stitching interferometer testing system

The most basic task in subaperture stitching test work is to confirm the precision of the system. We propose a method with which to calculate the system's precision. Statistical theory, especially regressive analysis, is employed. To discuss the statistical characteristics of all the random variables is the objective of the precision analyses. The results show that the number of sample points and the connatural error of the interferometer are the most important factors in the analyses.     

环形子孔径检测技术中测量数据的准确提取方法

环形子孔径拼接测试技术是一种无需辅助元件就能检测旋转对称大口径非球面镜的有效手段。根据该技术的检测原理及基于Zemike多项式的“拼接”算法,提出了一种相应的环形子孔径数据提取方法。该方法基于商用相移干涉仪的CCD成像系统和其数据处理软件提供的Mask编辑功能,利用被测镜面上方的三个可移动的基准标记进行绝对定位,给出了具体的实施方案。对一口径700mm、F2的抛物面主镜进行实验,研究结果表明,该数据提取方法操作简单可行,适合于加工车间的实施,取得了符合“拼接”算法需求的子孔径测试数据和对应环带的内外半径值。     

Iterative algorithm for subaperture stitching test with spherical interferometers

Recently we have proposed an iterative algorithm for subaperture stitching interferometry. It was referred to as the subaperture stitching and localization (SASL) algorithm. The limitation of the algorithm is that three-dimensional Cartesian coordinates are required, whereas the standard spherical interferometer can read out only the phase differences on the pixels. On the basis of the SASL algorithm, we propose an iterative algorithm for a spherical subaperture stitching test. It deals with data directly from the spherical interferometer. Unknown radii of best-fit spheres for a null test of subapertures are included in the optimization variables. The developed algorithm inherits the advantages of the SASL algorithm.     

Iterative algorithm for subaperture stitching interferometry for general surfaces

A novel iterative algorithm for subaperture stitching interferometry for general surfaces is presented. It is based on the alternating optimization technique and the successive linearization method. The computer-aided-design model of the tested surface is used to determine the overlapping region precisely. Subapertures are simultaneously stitched by minimizing deviations among them as well as deviations from the nominal surface. Precise prior knowledge of the six degrees-of-freedom nulling and alignment motion is no longer required.     

In-situ stitching interferometric test system for large plano optics

In-situ testing is an ideal technology for improving the precision and efficiency of fabrication. We developed an in-situ subaperture stitching interferometric test system for large plano optics in the workshop environment with high precision and satisfactory repeatability. In this paper, we provide a brief account of this system and the principle of insitu subaperture stitching measurement. Several validation tests are presented, which demonstrate that the developed system is capable of realizing in-situ testing. The size of optical flats can be measured is up to 420 mm×780 mm, and repeatability is smaller than 0.03λ. The paper also discusses the necessary requirements for a suitable workshop environment for ensuring that the tests are stable and reliable.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-018-0220-2     

Field stitching in thermal probe lithography by means of surface roughness correlation

A novel stitching method is presented which does not require special purpose alignment markers and which is particularly adapted to probe lithographic methods, enabling the writing of large patterns exceeding the size limitations imposed by high precision scan stages. The technique exploits the natural roughness of polymeric resist surfaces as a fingerprint marker for the sample position. Theoretical and experimental evidence is provided that sub-nanometer metrological accuracy can be achieved by inspecting the surface roughness in areas with 1?μm linear dimensions. The method has been put to the test in a thermal probe lithography experiment by writing a composite pattern consisting of five 10?μm ×?10?μm fields which are seamlessly joined together. The observed stitching error of 10?nm between fields is dominated by inaccuracies of the scanning hardware used in the experiment and is not fundamentally limited by the method per?se.     

Sampling error analysis of Shack–Hartmann wavefront sensor with variable subaperture pixels

Abstract

The sampling error of a Shack–Hartmann wavefront sensor with variable subaperture pixels is analysed under the consideration of various threshold values and detecting dynamic ranges. A generalized expression, which is used for fitting the sampling error of a Shack-Hartmann wavefront sensor with variable subaperture pixels, is presented. The computational results of the sampling error of a Shack–Hartmann wavefront sensor with different pixel numbers per subaperture, different detecting dynamic ranges, different atmospheric coherence length, different extended degree of the object and the different threshold values are also given. The results indicate that the sampling error of the Shack–Hartmann wavefront sensor is sensitive to the dynamic range of the subaperture, the pixel numbers per subaperture, the extended degree of the object and the coherent length of atmosphere, but not sensitive to the threshold value.     

Segmented mirror phasing using the focal-plane intensity

We develop a method for subaperture piston phase retrieval in a telescope using a segmented primary mirror. We assume that the mirror subapertures are arranged on a two-dimensional lattice, and in addition, the separate subaperture point-spread functions are focused and overlapped on the focal plane. Therefore, the residual errors are the subaperture piston phase errors, represented as a phasor, a unit modulus complex number, for each subaperture. Under these conditions, we find considerable simplicity in the calculated optical transfer function (OTF) at special subaperture lattice spatial frequencies. We then construct a phasor-based error function based on the modulus squared of the difference between the measured OTF and the calculated OTF. The remaining steps in our piston phase retrieval algorithms are developed by calculating the error-function variation, with respect to each phasor element. The resulting equations for the error gradient are then used iteratively, in a phasor-based algorithm, to find the minimum of the error function. In the applications, we simulate photon-noise-limited piston retrieval for a segmented primary with 18 hexagonal subapertures. When we invoke phase diversity, the piston retrievals prove unique and accurate.     

A Laser Scanner–Stage Synchronized System Supporting the Large-Area Precision Polishing of Additive-Manufactured Metallic Surfaces

This paper proposes a scanner–stage synchronized approach emphasizing a novel control structure for the laser polishing of Inconel 718 components manufactured by selective laser melting in order to address increasing demands for high surface quality in metal additive manufacturing. The proposed synchronized control system is composed of a motion decomposition module and an error synthesis module. The experimental results show that stitching errors can be avoided thanks to continuous motion during laser processing. Moreover, in comparison with the existing step-scan method, the processing efficiency of the proposed method is improved by 38.22% and the surface quality of the laser-polished area is significantly enhanced due to a more homogeneous distribution of the laser energy during the material phase change. The proposed synchronized system paves the way for high-speed, high-precision, and large-area laser material processing without stitching errors.     

长导轨直线度分段测量拼接方法研究

激光干涉仪测量超长导轨直线度时,因导轨长度超出干涉仪直线度测量范围,需分段测量后拼接,测量数据易受噪声和激光漂移等因素影响,导致拼接可能引入较大误差。通过分析拼接过程中的影响因素,结合长导轨结构特性,提出了一种将拼接公共点分布在相邻两节子导轨上,利用相邻两节子导轨夹角的稳定特性来实现长导轨直线度拼接的方法。通过仿真与实验,对比了30m范围内的直接测量法与坐标变换拼接法的测量结果,2种方法的直线度结果相差＜10μm,表明所提出的方法能有效减小拼接误差。将此方法应用于72m导轨的直线度测量,并与电子水平仪测量方法比较,2种方法结果相差10μm,表明所提出的方法可实现高精度的直线度拼接。     

印品检测过程中基于SIFT 算法缩小匹配范围的方法

针对多个CCD 采集多幅图像会产生一定的重叠区域,为了实现印品在线检测的要求,提出了一种结合SIFT 和缩小匹配范围的图像检测方法。该方法基于SIFT 提取特征点,改进了局部搜索范围,利用RANSAC 算法计算图像坐标变换矩阵,采用多分辨率融合方法对拼接图像进行融合处理。结果表明,采用该方法可以减少匹配和图像检验时间,降低估算概率,完成检测图像拼接。     

Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42?m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100?s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.     

利用帧间连贯性的动态地形可视化算法

针对动态地形图的特殊要求,利用帧间的连贯性给出了地形实时绘制可视化的解决方案.算法采用三角形二叉树的存储结构,利用嵌套误差判据球计算误差,避免T-连接和裂缝的产生.算法利用帧间连贯性,在相邻帧间只对渲染地形做局部调整,同时,又利用延迟判断时间进一步减少每帧所需判断的次数,提高了算法效率.实验结果表明,该算法有效地减少了计算量,能在满足地形实时绘制的同时很好的表现地形的形变效果.     

Testing fast aspheric convex surfaces with a linear array of sources

We describe a noncontact test procedure with which to obtain the shapes of fast convex surfaces. For this, an array of sources is positioned in a straight line and separated in such a way that the image by reflection on the surface consists of a set of equally spaced bright spots. By rotating the surface, we test different meridians such that, after 360 degrees, the entire surface is measured. We present the source array design and the surface evaluation algorithm. We found that, to reduce numerical error in the evaluation of the shape of the surface, a numerical integration must be performed by a method that uses parabolic arcs instead of the traditional method that uses trapezoids. Through some numerical simulations we analyzed the accuracy of the method by introducing random displacements into the measured data. We found that to measure the quality of the surface with accuracy better than 5 microm, we have to measure the coordinates of the centroids on the image plane with an accuracy better than 0.5 pixel, and we to have measure the positions of the linear sources with an accuracy better than 0.5 mm. Experimental results for the testing of a carbon fiber convex sphere of 383.6-mm diameter (f/0.398) are shown.     

缝合复合材料层板三维纤维弯曲模型及压缩强度预报

提出了三维纤维弯曲模型, 基于有限元法和周期性边界条件建立了缝合层板压缩强度分析方法, 采用桥联模型和最大应力判据分析损伤扩展并获得压缩强度, 预报结果与试验吻合较好。详细探讨了缝合参数对层合板压缩强度的影响规律, 结果表明: 缝合方向与表面纤维方向一致时, 较小的缝合针距和行距、较大的缝合线半径对压缩强度较为有利; 缝合方向与表面纤维方向垂直时, 较小的缝合针距和缝合线半径、较大的缝合行距对压缩强度较为有利。      

Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star

In an adaptive optics system with an undersampled Shack-Hartmann wave-front sensor (WFS), variations in seeing, laser guide star quality, and sodium layer thickness and range distance all combine to vary WFS centroid gain across the pupil during an exposure. While using the minimum of 4 pixels per WFS subaperture improves frame rate and read noise, the WFS centroid gain uncertainty may introduce static aberrations and degrade servo loop phase margin. We present a novel method to estimate and compensate WFS gains of each subaperture individually in real time for both natural and laser guide stars.     

二阶线性时不变测量系统动态特性的补偿与动态不确定度评估

采用一种新的设计测量系统补偿滤波器的方法,根据校准得到的测量系统频率响应数据直接设计补偿滤波器,避免了系统辨识过程。通过接近实际测量条件的仿真实验表明,该方法能有效地提高测量系统的带宽,减小动态误差。同时,按照GUM推荐的不确定度评定准则,对整个动态测量过程,包括动态补偿以及滤波运算过程的不确定度进行了评估,得到了经过补偿后系统输出的被测量以及对应的动态不确定度曲线。     

Field-of-view limitations of phased telescope arrays

The optical performance of imaging phased telescope arrays is degraded by various design, manufacturing, and operational errors. Perhaps the most basic and fundamental of these error sources are the residual aberrations of the optical design chosen for the individual telescopes. We show that third-order field curvature and distortion, which are rather benign aberrations in a conventional telescope, result in relative phase and tilt errors between the individual telescopes making up the array. The field-dependent image degradation caused by these relative phase and tilt errors is then predicted for different subaperture configurations and telescope design parameters. For phased arrays made up of simple two-mirror telescopes, distortion limits the field of view to less than 5 arcmin for small subapertures (D < 0.5 m), and field curvature limits the field of view to less than 1 arcmin for subaperture diameters greater than 2 m. Quantitative parametric results yielding tolerances for residual field curvature as the phased array is scaled up in size are presented graphically. If a 0.5-deg field of view is desired for telescope diameters greater than 2 m, complex telescope configurations are necessary to satisfy the rather tight tolerances on both field curvature and distortion.